Whether discovery of a planet having a non-elliptical orbit pose a challenge to Kepler’s first law, Newton’s laws, neither, or both.

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I've uploaded these questions a few times now as I'm a little confused about its dependent & independent variables these are the two Answer I've received back Answer 1. The dependent variables are Pressure→P volume→ (V) No. of moles→ n arbitrary constants a and b varies gas to gas. Independent variable: R→Universal gas constant Answer 2. Dependent variable: V,T,P. Independent Variable a,b,n,R I would like to know detailed reasoning behind these variables in these 2 answers and which one is the correct answer and also if there is a 3rd answer please let me know the reasoning behind that as well as solve the rest of the question.

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Chapter 19, Problem 26PQ

To determine

Whether discovery of a planet having a non-elliptical orbit pose a challenge to Kepler’s first law, Newton’s laws, neither, or both.

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I've uploaded these questions a few times now as I'm a little confused about its dependent & independent variables these are the two Answer I've received back Answer 1. The dependent variables are Pressure→P volume→ (V) No. of moles→ n arbitrary constants a and b varies gas to gas. Independent variable: R→Universal gas constant Answer 2. Dependent variable: V,T,P. Independent Variable a,b,n,R I would like to know detailed reasoning behind these variables in these 2 answers and which one is the correct answer and also if there is a 3rd answer please let me know the reasoning behind that as well as solve the rest of the question.

Under what conditions of volume does a van der Waals gas behave like an ideal gas? Use the van der Waals equation of state to justify your answer.

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